Mayer cluster

Theoretical investigations of quenched-annealed systems have been initiated with success by Madden and Glandt [15,16] these authors have presented exact Mayer cluster expansions of correlation functions for the case when the matrix subsystem is generated by quenching from an equihbrium distribution, as well as for the case of arbitrary distribution of obstacles. However, their integral equations for the correlation functions... 

Note added in -proof. The application of the usual integral equation theories of the liquid state 2> to water has not been successful.1) A recent study by H. C. Andersen [J. Chem. Phys. 61, 4985 (1974)] promises to change this situation. Briefly, Andersen reformulates the well known Mayer cluster expansion of the distribution function 2> by consistently taking into account the saturation of interaction characteristic of hydrogen bonding. Approximations are selected which satisfy this saturation condition at each step of the analysis. Preliminary calculations (H. C. Andersen, private communication) indicate that even low order approximations that preserve the saturation condition lead to qualitative be-... 

In these remarks, one can see a pioneering suggestion of a cluster mixture theory of liquids with short-range (exchange-like) forces, along the lines of Mayer cluster theory (Sidebar 13.5) or quantum cluster equilibrium theory (Section 13.3.4). 

A more practical discussion is given in Section 2.3. At this point, let us mention the Mayer cluster expansion technique originally applied to the imperfect gas [J.E. Mayer, M. Mayer (1940)] but to which Allnatt and Lidiard [A. R. Allnatt, A.B. Lidiard (1993)] have drawn attention in the present context. In this approach, In 2... 

Note that the introduction of structural conditions and site exclusions suffices to obtain (apparent) interaction parameters, which differs from the concept of the Mayer cluster expansion approach. 

Our general approach is a proper adaptation and generalization of the gas-type theories of McMillan and Mayer and of Kirkwood and Buff. These were originally developed for simple (monomer) solutions. We use the cluster development of McMillan and Mayer, which itself is an adaptation of the original (Ursell)-Mayer cluster development. We... 

Somewhat simplified version of the Mayer cluster expansion theory for a single component gas has been presented by E. E. Salpeter in Annals of Physics 5, 183 (1958). There some of the combinatorial algebra is replaced by topological considerations. 

The thermodynamics of a l-d Fermi system can be perfectly mapped onto the thermodynamics of a two-component classical real gas on the surface of a cylinder. The relationship between these two infrared problems (cf. Zittartz s contribution) is exploited as follows. We treat the classical plasma by a modified Mayer cluster expansion method (the lowest order term corresponding to the Debye Hiickel theory), and obtain an exponentially activated behavior of the specific heat (cf. Luther s contribution) of the original quantum gas by simply reinterpreting the meaning of thermodynamic variables. 

Note that (6.23) differs from the expression given in Section 1.8. The latter is obtained from the former if the total potential energy C/3(Xi, X2, X3) is pairwise additive. Equations (6.22) and (6.23) are special cases of a more general scheme which provides relations between virial coefficients and integrals involving interactions among a set of a small number of particles. This is known as the Mayer cluster theory [see, for example, Mayer and Mayer (1940), Hill (1956), and Munster (1969)]. 

The paper by Montroll and Yu makes use of a general formalism for the investigation of the properties of lattices with two types of component, type I and type II. The formalism is in the spirit of the Mayer cluster integral approach. Let us consider a pure type 1 component lattice with the effect of the type II components imposed upon it. Type II components are considered first as single units, then as pairs, triples, etc. For the DNA problem, the pure lattice is a one-dimensional string of A-T (or G-C) base pairs, witli the G-C (or A-T) base pairs acting as the type II components. 

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